Maths Surds and Indices irrational numbers etc.

If you wanted to write 0.4545454545454... as a fraction;

x= 0.45454545454..

100x = 45.454545454...

(takeaway x) 99x= 45 so 0.454545454.. = 45/99

adding and subtracting

4Ö7 - 2Ö7 = 2Ö7 like 3Öa - 2Öa = 1Öa
5Ö2 + 8Ö2 = 13Ö2 like 3Öa + 3Öa = 6Öa

you cant add or subtract surds that are not the same. eg you cant add Öa + Öb because they are not the same, you would have to change it so that both surds are the same befor you could add. (look at aqa november 2006 practice paper, there is a question similar)

multiplying (just example)

Ö5 × Ö15 = Ö75 (= Ö(15 × 5))
= Ö25 × Ö3 (simplifing iy back down - use square numbers)
= 5Ö3.

rationalising denominators
1/ Ö2 first you have to times both sides by Ö2 so Ö2 /Ö2 Ö2

Ö2 Ö2 = Ö4 = 2

so rationalised Ö2/4